PUV test with multiple reflection coefficients

swash/processing/r_test.py

@@ -4,7 +4,7 @@ from numpy import random
 import scipy.signal as sgl
 
 yi = random.normal(size=2**20)
-yr = 0.3 * np.roll(yi, -(2**10))
+yr = np.roll(yi, -(2**10))
 
 figy, axy = plt.subplots()
 axy.plot(np.arange(2**10, 2**11), yi[2**10 : 2**11])
@@ -14,8 +14,8 @@ figf, axf = plt.subplots()
 axf.plot(*sgl.welch(yi))
 axf.plot(*sgl.welch(yr))
 
-eta = yi + yr
-u = -yi + yr
+eta = lambda r: yi + r * yr
+u = lambda r: -yi + r * yr
 
 
 def puv(eta, u):
@@ -30,21 +30,20 @@ def puv(eta, u):
 
 figr, axr = plt.subplots()
 
-axr.plot(*puv(eta, u), label="Without noise")
-axr.plot(
-    *puv(
-        eta + 0.4 * random.normal(size=2**20), u + 0.4 * random.normal(size=2**20)
-    ),
-    label="With noise"
+for r in np.arange(0, 1.1, 0.1):
+    axr.plot(*puv(eta(r), u(r)), c="k")
+    Rn = puv(
+        eta(r) + 0.4 * random.normal(size=2**20),
+        u(r) + 0.4 * random.normal(size=2**20),
     )
+    axr.plot(
+        *Rn,
+        c="#ff6600",
+    )
+    axr.annotate(f"{r=:.1f}", (Rn[0][0], Rn[1][0]), bbox={"boxstyle": "square", "facecolor": "w"})
 axr.grid()
 axr.autoscale(True, "x", tight=True)
 axr.set(ylim=(0, 1), ylabel="R", xlabel="f")
-axr.legend(loc="lower left")
-
-axpsd = axr.twinx()
-axpsd.plot(*sgl.welch(eta), label=r"PSD ($\eta$)", c="k", alpha=0.2, lw=1)
-axpsd.legend(loc="lower right")
-axpsd.set(ylabel="PSD")
+axr.legend(("No noise", "40% noise"), loc="lower left")
 
 plt.show()